Exploring the Constant of Proportionality

Mr. Boer explains the concept of the constant of proportionality, also known as the unit rate, in proportional relationships. He demonstrates how to find this constant using tables, equations, and graphs. The constant is the ratio of y to x, and it can be identified in equations as the coefficient of x. In graphs, the constant is determined by selecting a point on the line and calculating the ratio of y to x.

What does the constant of proportionality represent in a proportional relationship?

• A constant difference

• A varying ratio

• A variable rate

• A constant ratio or unit rate

In the formula 'y = kx', what does 'k' stand for?

• The sum of x and y

• The constant of proportionality

• The variable y

• The variable x

Why do we use 'k' to represent the constant of proportionality?

• Because it represents the keyword 'constant'

• Because 'k' is a traditional symbol for constants in mathematics

• Because it stands for 'constant'

• Because it is the first letter of 'knowledge'

How can you find the constant of proportionality from a table?

• Multiply any y-value by its corresponding x-value

• Add any y-value to its corresponding x-value

• Divide the sum of y-values by the sum of x-values

• Divide any y-value by its corresponding x-value

What is the constant of proportionality if y = 24 when x = 2?

• 12

• 2

• 48

• 24

In the equation 'y = 5x', what is the constant of proportionality?

• 0

• y

• x

• 5

What is the constant of proportionality in the equation 'y = 3x'?

• 0

• y

• x

• 3

If the equation is 'y = 1/4x', what is the constant of proportionality?

• 1/4

• 4

• x

• y

How do you find the constant of proportionality from a graph?

• By dividing the y-coordinate of any point by its x-coordinate

• By adding the x and y coordinates of any point

• By finding the slope of the line

• By dividing the x-coordinate of any point by its y-coordinate

What is the constant of proportionality if a point on the graph has coordinates (1, 4)?

• 1

• 0.25

• 5

• 4